提出快速核方法实现精准预测区间，速度提升40倍且区间更短。
SpeedCP: Fast Kernel-based Conditional Conformal Prediction
- 基于核函数路径追踪，高效求解正则化优化问题。
- 相比前人方法区间长度缩短30%，计算速度提升40倍。
- 适用于高维黑箱模型，自动调节超参数并保证条件覆盖性。
置信预测可提供无需分布假设的预测集，并具有有限样本下的条件保证。本文基于Gibbs等（2023）提出的基于再生核希尔伯特空间（RKHS）的框架，该框架利用协变量偏移族实现近似条件置信区间，虽具强大理论潜力，但计算成本极高。为弥合这一差距，我们提出一种稳定高效的算法，以几乎与单次核分位数拟合相当的成本计算正则化RKHS置信优化问题的完整解路径。该路径追踪框架同时完成超参数调优，实现平滑性控制与数据自适应校准。为拓展至高维场景，进一步结合低秩潜在嵌入，使条件有效性在数据驱动的潜空间中得以保留。实证结果表明，本方法在多种现代黑箱预测器上均实现可靠条件覆盖率，相比Gibbs等（2023）方法将区间长度缩短30%，同时获得40倍加速。
原文摘要 · Abstract (English)
Conformal prediction provides distribution-free prediction sets with finite-sample conditional guarantees. We build upon the RKHS-based framework of Gibbs et al. (2023), which leverages families of covariate shifts to provide approximate conditional conformal prediction intervals, an approach with strong theoretical promise, but with prohibitive computational cost. To bridge this gap, we develop a stable and efficient algorithm that computes the full solution path of the regularized RKHS conformal optimization problem, at essentially the same cost as a single kernel quantile fit. Our path-tracing framework simultaneously tunes hyperparameters, providing smoothness control and data-adaptive calibration. To extend the method to high-dimensional settings, we further integrate our approach with low-rank latent embeddings that capture conditional validity in a data-driven latent space. Empirically, our method provides reliable conditional coverage across a variety of modern black-box predictors, improving the interval length of Gibbs et al. (2023) by 30%, while achieving a 40-fold speedup.
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